Research Question: Are female employees discriminated against in promotion decisions made by male managers?
Rows: 48
Columns: 2
$ sex <fct> male, male, male, male, male, male, male, male, male, male, male, male, male, mal…
$ decision <fct> promoted, promoted, promoted, promoted, promoted, promoted, promoted, promoted, p…
decision
sex promoted not promoted
male 21 3
female 14 10
decision
sex promoted not promoted
male 0.8750000 0.1250000
female 0.5833333 0.4166667
Describe the apparent association between the variables
sex and decision.
Do you think these proportions indicate evidence of discrimination, or could they just be showing chance variation due to the random components of the study (e.g., sampling and assignment of the supervisors)? How are you deciding?
Statistics:
Parameters:
Hypotheses:
The observed statistic is in the direction of the alternative hypothesis, but there are two possibilities:
sex decision
male :24 promoted :35
female:24 not promoted:13
The simulation-based P-value is the proportion of simulated statistics that were as extreme or more extreme than the observed statistic.
The smaller the P-value, the more evidence you have against \(H_0\) in favor of \(H_A\).
The P-value is the probability, assuming \(H_0\), that an identical study would produce statistics as extreme as the statistics you observed.
https://www.rossmanchance.com/applets/2021/chisqshuffle/ChiSqShuffle.htm?dolphins=1
The applet shows you a contingency table and a standardized barplot of the dolphin data. Record the observed difference in proportions \(\hat{p}_\text{dolphin} - \hat{p}_\text{control}\) between the treatment group and the control group.
Check the box for Show Shuffle Options. Click the Shuffle button and observe what happens. Click it a couple more times and observe.
Enter 1000 in the Number of Shuffles box and click Shuffle. Use the Count Samples box to count the number of samples that are more extreme than the observed statistic (enter the observed statistic in the box and click Count). Record the proportion that are more extreme (i.e., the P-value).
Do you think the study is just showing random variation, or do you think the treatment group is showing significantly better improvement than the control group?
Researchers followed a random sample of 30 penguins for a period of time. Some were banded, some not. They recorded whether they were still alive at the end of the time period.
Return to the applet, and click on the link for Penguin study.
Check the box for Show Shuffle Options. Enter 1000 in the Number of Shuffles box and click Shuffle. Use the Count Samples box to count the number of samples that are more extreme than the observed statistic (enter the observed statistic in the box and click Count). Record the proportion that are more extreme (i.e., the P-value).
Do you think the study is just showing random variation, or do you think there is a significant difference in the survival rates between banded and non-banded penguins?
Research Question: Are students influenced by advice about being prudent with their money?
\(H_0:\) Null hypothesis. Reminding students that they can save money for later purchases will not have any impact on students’ spending decisions.
\(H_A:\) Alternative hypothesis. Reminding students that they can save money for later purchases will reduce the chance they will continue with a purchase.
Rows: 150
Columns: 2
$ group <fct> control, control, control, control, control, control, control, control, control, …
$ decision <fct> buy video, buy video, buy video, buy video, buy video, buy video, buy video, buy …
decision
group buy video not buy video
control 56 19
treatment 41 34
decision
group buy video not buy video
control 0.7466667 0.2533333
treatment 0.5466667 0.4533333
Observed statistic: \(\hat{p}_C - \hat{p}_T \approx 0.746 - 0.546 = 0.2\)
group decision
control :75 buy video :97
treatment:75 not buy video:53